Results 41 to 50 of about 5,049 (220)
Fractal and Fractional, 2023 In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function.
Yuri Dimitrov +2 more
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Fractional variational iteration method and its application to fractional partial differential equation [PDF]
, 2013 We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense.
Elbeleze, Asma Ali +2 more
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Discrete Dynamics in Nature and Society, 2020 The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an
Ndolane Sene +3 more
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On a Multigrid Method for Tempered Fractional Diffusion Equations
Fractal and Fractional, 2021 In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation.
Linlin Bu, Cornelis W. Oosterlee
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The Valuation of European Option Under Subdiffusive Fractional Brownian Motion of the Short Rate [PDF]
, 2020 In this paper, we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze European option in a fractional Black–Scholes environment, when the short rate follows the subdiffusive fractional Black–Scholes model. We derive a
Shokrollahi, Foad
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Solving Black-Schole Equation Using Standard Fractional Brownian Motion
Journal of Mathematics Research, 2019 In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different ...
Didier Alain Njamen Njomen +1 more
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Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance
Mathematics, 2023 In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the ...
Malik Zaka Ullah +3 more
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Martingale Option Pricing [PDF]
, 2007 We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price.
Bassler, K. E. +2 more
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Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method
Abstract and Applied Analysis, 2013 This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative.
Lina Song, Weiguo Wang
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Approximate Solution for Fractional Black-Scholes European Option Pricing Equation
Al-Mukhtar Journal of Sciences, 2023 The Black-Scholes equation is one of the most significant mathematical models for a financial market. In this paper, the homotopy perturbation method is combined with Mohand transform to obtain the approximate solution of the fractional Black-Scholes European option pricing equation. The fractional derivative is considered in the Caputo sense.
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